Resolution of initial-state in security applications of DES

Abstract

A non-deterministic labeled finite automaton is initial-state opaque if the membership of its true initial state to a set of secret states S remains opaque (i.e., uncertain) to an intruder who observes system activity through some natural projection map. The verification of initial-state opacity has been shown to be a PSPACE-complete problem by establishing that it is equivalent to the language containment problem. In this paper we take a slightly different viewpoint and try to assess the ability of a user (who is dictating the activity in the system and indirectly the observations generated) to avoid revealing to the outside observer that the initial state of the system lied within the set of secret states S. A system that does not allow the user to act indefinitely in such a way is said to posses the property of resolution of initial state with respect to S. We show that in discrete event systems that can be modeled as non-deterministic labeled finite automata, this property can be verified with polynomial complexity in a way that resembles the verification of diagnosability.